VocabularyMonomial – Polynomial with 1 term.Binomial – Polynomial with 2 terms.Trinomial – Polynomial with 3 terms.
VocabularyMonomial – a number, a variable with a positive integer exponent, or the product of a number and one or more variables with positive integer exponents.Degree of a monomial – sum of the exponents of the variables in the monomial
VocabularyPolynomial – a monomial or a sum of monomials, each called a term of the polynomial.Degree of a polynomial – the greatest degree of its terms.Leading coefficient – the coefficient of the highest degree term.
Example 1 Rewrite a polynomialWrite 15x – x3 + 3 so that the exponents decrease fromleft to right. Identify the degree and leading coefficientof the polynomial.SOLUTIONThe polynomial can be written as – x3 + 15x + 3 . Thetable shows the degree of each term. The greatestdegree is 3, so the degree of the polynomial is 3, andthe leading coefficient is –1. Term – x3 15x 3 Degree 3 1 0
Example 2 Identify and classify polynomialsTell whether the expression is a polynomial. If it is apolynomial, find its degree and classify it by the numberof its terms. Otherwise, tell why it is not a polynomial. Classify by degree Expression Is it a polynomial? and number of termsa. 9 Yes 0 degree monomialb. 2x2 + x – 5 Yes 2nd degree trinomialc. 6n4 – 8n No; variable exponentd. n–2 – 3 No; negative exponente. 7bc3 + 4b4c Yes 5th degree binomial
Adding & Subtracting PolynomialsTo add polynomials, combine like terms.To subtract a polynomial, add its oppositeTo find the opposite of a polynomial, multiply each of its terms by -1
Example 3 Add and subtract monomialsFind the sum or difference.a. – 3b2 + 7b2 = 4b2 Combine like terms.b. 2xy – 5xy = 2xy + (– 5xy ) Rewrite as a sum. = – 3xy Combine like terms.
Example 4 Add polynomialsFind the sum ( 3x2 + x – 6 ) + ( x2 + 4x + 10 ).SOLUTIONGroup like terms and simplify. ( 3x2 + x – 6 ) + ( x2 + 4x + 10 ) = ( 3x2 + x2 ) + ( x + 4x) + (–6 + 10 ) = 4x2 + 5x + 4